"An Efficient Second Order in Time Scheme for Approximating Long Time S" by Xiaoming Wang
 

Abstract

We investigate the long-time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equations in a periodic box: The scheme is a combination of a 2nd-order in time backward-differentiation and a particular explicit Adams-Bashforth treatment of the advection term. Therefore, only a linear constant coefficient Poisson solver is needed at each time step. We prove uniform in time bounds on this scheme in L 2, H per1 and H per2 provided that the time-step is sufficiently small. These time uniform estimates further lead to the convergence of long-time statistics (stationary statistical properties) of the scheme to that of the NSE itself at vanishing time-step. © 2012 Springer-Verlag.

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

0029-599X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 Springer, All rights reserved.

Publication Date

01 Aug 2012

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